e211test1

# e211test1 - TEST 1 STATICS FORMULAS VECTOR ALGEBRA Vector...

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TEST 1 STATICS FORMULAS Page 1 VECTOR ALGEBRA Vector Addition, Three Dimensions v k F j F i F F Z Y X ˆ ˆ ˆ + + = Cartesian components of a vector F , where . ) cos( ), cos( ), cos( Z Z Y Y X X F F F F F F θ θ θ= = = v k S F j S F i S F S F R Z Z Y Y X X ˆ ) ( ˆ ) ( ˆ ) ( + + + + + = + = v v Vector addition by components. R R R R R R R R R R Z Z Y Y X X Z Y X = = = + + = ) cos( , ) cos( , ) cos( , ) ( ) ( ) ( 2 2 2 θ θ θ Vector Addition, Two Dimensions v j F i F F Y X ˆ ˆ + = Cartesian components of a vector F , where , where θ is the angle from the horizontal . ) sin( ), cos( Y Y X F F F F θ = j S F i S F S F R Y Y X X ˆ ) ( ˆ ) ( + + + = + = v v v Vector addition by components. X Y Y X R R R R R = + = ) tan( , ) ( ) ( 2 2 θ Unit vector λ k j i Z Y X ˆ cos ˆ cos ˆ cos θ θ θ λ + = + The unit vector is unit-less ! Direction vector with start point A and endpoint B. v Z Z Y Y X X AB A B A B A B D = , , Make sure you keep start point and endpoint consistent. Vector Cross Product (Vector Product) V = P X Q , V = PQ sin θ , where θ is the angle between the two vectors V and Q . V X = P Y Q Z – P Z Q Y V Y = P Z Q X – P X Q Z VZ = P X Q Y – P Y Q X , or use the determinate expansion method: Z Y X Z Y X Q Q Q P P P k j i ˆ ˆ ˆ = V

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e211test1 - TEST 1 STATICS FORMULAS VECTOR ALGEBRA Vector...

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